Relativistic length, 2 viewpoints

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SUMMARY

The discussion centers on the relativistic perception of length between two cyclists moving at velocities close to the speed of light, Va and Vb. It establishes that the relative speed formula, V = (Va + Vb) / (1 + (Va * Vb / c^2)), and the relative length formula, l = lo * √(1 - (V/c)^2), yield the same results for both cyclists regarding their perceived lengths, La and Lb. The conclusion asserts that both cyclists perceive each other as the same length, provided they start with identical lengths, lo. The concept of simultaneity loss is also introduced, emphasizing its significance in relativistic scenarios.

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  • Understanding of special relativity principles
  • Familiarity with the Lorentz transformation
  • Knowledge of relativistic velocity addition
  • Basic grasp of the concept of simultaneity in physics
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This discussion is beneficial for physicists, students of physics, and anyone interested in the implications of special relativity on perception and measurement at high velocities.

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Problem statement:

Two identical cyclists ride past each other with constant velocities Va and Vb, which are close to the speed of light. Can it be that cyclist A perceives cyclist B as shorter or longer that cyclist B perceives cyclist A ? Or simply La is NOT equal to Lb ? (La-length of cyclist A as seen by cyclist B, Lb -length of cyclist B as seen by cyclist A).

Relevant formulas:

Relative speed V = Va+Vb/(1+(Va*Vb/c^2))
Relative length l = lo * square root from 1-(V/c)^2

Conclusion:

The V from the second equation is equal for both cyclists, since addition and multiplication are alternate. lo is also equal. So there is no difference in the way cyclists A and B see each other.

Is this conclusion right?
 
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its correct if the cyclists are the same length to begin with.

dont forget that there is also a loss of simultaneity. once you factor that in it stops seeming so impossible.
 
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